A kinematic calibration and positioning error compensation method considering mechanism deformation

Abstract

A kinematic calibration and positioning error compensation method that takes into account the deformation of the mechanism can be used to improve the accuracy of robot positioning operations. The deformation is calculated using the superposition method, and the deformation difference is calculated in combination with finite element simulation analysis. The numerical analysis software is used to fit the interpolation curve to establish a deformation model; based on the deformation model, the particle swarm algorithm is used to calculate the corresponding posture error. Based on the multi-body dynamics modeling analysis, the force acting on the telescopic rod ball joint and the friction force at the follower moving pair are analyzed to further calculate the corresponding posture error. The posture errors are added together to obtain the posture error caused by elastic deformation. During the calibration test, the posture error caused by the structural error is separated from the posture error caused by the elastic deformation of the mechanism to improve the identification accuracy; during the error compensation, the posture error caused by the deformation of the mechanism is considered, and the target posture is re-positioned to improve the compensation accuracy; further, a machine learning method is used to establish a correlation between the target positioning posture and the motion of the moving pair. The method of the present invention is simple and easy to implement, which is conducive to improving the accuracy of robot operations and meeting the accuracy requirements of intelligent assembly.

Description

Technical Field

[0001] The present invention relates to a kinematic calibration and positioning error compensation method, in particular to a precise positioning technology for complex systems, specifically a kinematic calibration and positioning error compensation method that takes mechanism deformation into consideration, which can be used to improve the operating accuracy in the field of robot positioning. Background Art

[0002] CNC machine tools typically consist of an end effector and an attitude adjustment mechanism. Among these mechanisms, those based on POGO columns offer advantages such as good reconfigurability and high rigidity, and are increasingly being used in intelligent assembly. Parallel attitude adjustment systems, consisting of a work platform connected to multiple POGO columns, are particularly well-suited for adjusting the position and orientation of parts during assembly in the mechanical field.

[0003] The work platforms used in some intelligent assembly fields are relatively large. Under the action of their own weight, the platform itself and the telescopic rods supporting the platform will undergo elastic deformation. Elastic deformation is related to the spatial posture, load size and direction of each component of the system. The amount of deformation varies under different spatial postures, which will affect the positioning accuracy of the parallel attitude adjustment system. For the parallel attitude adjustment system based on POGO columns, due to the influence of elastic deformation, corresponding kinematic calibration and positioning error compensation strategies need to be formulated. The posture error calculated using data collected by the measuring equipment during calibration is the result of the combined effect of structural error and elastic deformation error. Some researchers did not separate the posture error caused by structural error from the posture error caused by elastic deformation during error identification, which reduced the accuracy of structural error identification.

[0004] The elastic error analysis takes into account that the working platform and telescopic rod of the system are actually flexible parts, which in turn affects the positioning accuracy of the parallel attitude adjustment system. The calculation of the attitude error can be carried out through finite element simulation and mathematical modeling. Summary of the Invention

[0005] The purpose of this invention is to address the low positioning accuracy of existing parallel attitude adjustment systems by developing a kinematic calibration and positioning error compensation method that considers mechanism deformation. This method considers the influence of posture errors caused by elastic deformation of the work platform and telescopic rod. During structural error identification and posture compensation, the posture error sources are separated and the target posture is repositioned, improving the accuracy of structural error identification and positioning error compensation. Machine learning methods are used to train the parallel attitude adjustment system's autonomous high-precision positioning capabilities.

[0006] The technical solution of the present invention is: a kinematic calibration and positioning error compensation method considering the deformation of the mechanism, using the superposition method to calculate the deflection of each point of the simply supported beam, comparing the calculation results of the superposition method with the finite element simulation results, calculating the deformation difference and compensating it, combining the particle swarm algorithm to calculate the posture error caused by the deformation of the working platform; based on the multi-body dynamics modeling method, analyzing the force acting on the telescopic rod and the friction force at the follower moving pair; calculating the deformation of the telescopic rod and the posture error caused by the force acting on the telescopic rod according to the supporting force acting on the telescopic rod; calculating the deformation of the telescopic rod according to the friction force at the follower moving pair, and then calculating the posture error caused by the friction force; adding the posture errors caused by gravity, friction and supporting force to obtain the posture error caused by elastic deformation. ; Use the total posture error to subtract the posture error caused by elastic deformation to obtain the posture error caused by structural error; input the posture error caused by structural error into the error model for kinematic calibration and structural error identification; subtract the identified structural error from the ideal structural parameters to obtain the corrected structural parameters; Considering the influence of the posture error caused by elastic deformation, the target posture is corrected, that is, the posture error caused by elastic deformation is subtracted from the ideal target posture to obtain the target posture of secondary positioning; On the basis of the corrected structural parameters, combined with the target posture of secondary positioning, kinematic inverse solution is performed to control the motion of each moving pair and perform error compensation; Use machine learning methods to establish the correlation between the target positioning posture and the motion of the moving pair, and train the parallel posture adjustment system's autonomous high-precision positioning capability.

[0007] The specific steps of this technical solution are: (1) using the superposition method to calculate the deflection of each point of the simply supported beam; comparing the calculation results of the superposition method with the finite element simulation results, and calculating the deformation difference; using numerical analysis software to fit the deformation difference curve; and calculating the posture error caused by the deformation of the working platform.

[0008] (2) Use the multi-body dynamics modeling method to perform dynamic modeling; calculate the force acting on the spherical joint; calculate the spatial position change of the spherical joint through the driving force; based on the deformation, use the least squares method to calculate the posture error caused by the position change of the spherical joint point.

[0009] (3) Based on the multi-body dynamics model, the following error of the follower moving pair is calculated; based on the following error, the posture error caused by the following error is calculated.

[0010] (4) Ignoring the higher-order terms in the pose error, the pose errors caused by steps (1), (2), and (3) are added together to obtain the pose error caused by elastic deformation.

[0011] (5) The pose error caused by structural error is separated from the pose error caused by elastic deformation, and then kinematic calibration is performed; the influence of high-order terms is ignored, and the pose error matrix caused by elastic deformation is subtracted from the total pose error matrix to obtain the pose error matrix caused by structural error.

[0012] (6) Considering the influence of the posture error caused by elastic deformation, the target posture is re-positioned; the secondary positioning method is to subtract the posture error matrix caused by elastic deformation from the target posture matrix.

[0013] (7) The ideal structural parameters minus the identified structural errors are used to obtain the corrected structural parameters, i.e., the actual structural parameters.

[0014] (8) Based on the corrected structural parameters, perform kinematic inverse analysis to control the motion of each moving pair and perform error compensation.

[0015] (9) Furthermore, machine learning methods are used to establish the correlation between the target positioning posture and the motion of the moving pair, and to train the parallel attitude adjustment system's autonomous high-precision positioning capability.

[0016] The beneficial effects of the present invention are as follows: the present invention proposes an analytical calculation method for the deformation of a mechanism under multiple spatial postures, which improves the calculation accuracy and efficiency of the posture error caused by elastic deformation. Combined with the kinematic calibration and positioning error compensation method, it can effectively improve the spatial positioning accuracy of the parallel posture adjustment system. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 Schematic diagram of the parallel attitude adjustment system considering mechanism deformation.

[0017] Figure 2 Implementation process.

[0018] Figure 3 This is the three-dimensional model of the parallel attitude adjustment system. DETAILED DESCRIPTION The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0019] like Figure 3 As shown, the parallel posture adjustment system consists of 4 POGO columns (locators) and 1 working platform: POGO column 1 (locator 1) is designed only with z Towards active moving pair; POGO column 2 (locator 2) is designed with x Towards, z Towards active moving pair; POGO columns 3, 4 (locators 3, 4) are designed with x、y、z Three-direction moving pair, among which, z The direction is the active moving pair (driven by a servo motor), x、 yThe direction is a follower moving pair (a moving pair without motor drive, which moves under the action of the system's internal force). Each POGO column (locator) is connected to the work platform through a spherical joint. Under the action of gravity, support force at the spherical joint, and friction, the parallel attitude adjustment system will undergo elastic deformation, such as Figure 1 shown.

[0020] A kinematic calibration and positioning error compensation method considering mechanism deformation, such as Figure 2 As shown, the specific steps are:

[0021] (1) Use the superposition method to calculate the deflection of each point on the simply supported beam; compare the calculation results of the superposition method with the finite element simulation results to calculate the deformation difference; use numerical analysis software to fit the deformation difference curve; calculate the posture error caused by the deformation of the work platform.

[0022] (2) Use the multi-body dynamics modeling method to perform dynamic modeling; calculate the force acting on the spherical joint; calculate the spatial position change of the spherical joint through the driving force; based on the deformation, use the least squares method to calculate the posture error caused by the position change of the spherical joint point.

[0023] (3) Based on the multi-body dynamics model, the following error of the follower moving pair is calculated; based on the following error, the posture error caused by the following error is calculated.

[0024] (4) Ignoring the higher-order terms in the pose error, the pose errors caused by steps (1), (2), and (3) are added together to obtain the pose error caused by elastic deformation.

[0025] (5) The pose error caused by structural error is separated from the pose error caused by elastic deformation, and then kinematic calibration is performed; the influence of high-order terms is ignored, and the pose error matrix caused by elastic deformation is subtracted from the total pose error matrix to obtain the pose error matrix caused by structural error.

[0026] (6) Considering the influence of the posture error caused by elastic deformation, the target posture is re-positioned; the secondary positioning method is to subtract the posture error matrix caused by elastic deformation from the target posture matrix.

[0027] (7) The ideal structural parameters minus the identified structural errors are used to obtain the corrected structural parameters, i.e., the actual structural parameters.

[0028] (8) Based on the corrected structural parameters, perform kinematic inverse analysis to control the motion of each moving pair and perform error compensation.

[0029] (9) Furthermore, machine learning methods are used to establish the correlation between the target positioning posture and the motion of the moving pair, and to train the parallel attitude adjustment system's autonomous high-precision positioning capability.

[0030] A kinematic calibration and positioning error compensation method considering the deformation of the mechanism is described in detail as follows: (1) When analyzing the posture error caused by gravity, it is necessary to first analyze the spatial position change of the positioning point of the work platform under the action of gravity, and then analyze the corresponding deformation error based on the spatial position change of the positioning point. First, simulate it with finite element software, and then use mathematical modeling methods such as superposition method to fit the coordinate change law. During fitting, the coordinate system of the work platform is O t - x t y t z t Relative to the global coordinate system O b - x b y b z b The posture transformation matrix is R , then the global coordinate system O b - x b y b z b Relative to the work platform coordinate system O t - x t y t z t The posture transformation matrix is R −1 ; The inverse of the rotation matrix is ​​equal to the transpose of the rotation matrix. The uniform force is expressed in the work platform coordinate system as: R −1 q ( R T q ) ， Right now:

[0031]

[0032] in, q represents the uniform force, α 、 βIndicates the rotation angle of the global coordinate system of the work platform relative to the ground. Finite element simulation software is used to analyze the coordinate changes of the positioning points of the work platform in different positions. During the simulation analysis, displacement constraints are applied to the connection between the work platform and the positioner. The deformation amount is compared using finite element simulation software. The difference between the deformation analysis method and the finite element simulation software analysis results is compared by comparing the spatial position changes of the points, and then the deformation analysis method is corrected. When correcting, numerical analysis software is used to fit the difference using polynomial fitting. d . x Interpolation d x Use the following formula to calculate:

[0033] d x = k 3 x 3 + k 2 x 2 + k 1 x

[0034] Where, k 1. k 2. k 3 represents the coefficient, x Indicates a point x The coordinate value in the direction. Similarly, the difference in other directions is calculated d y 、 d z , and further conclude that the spatial position change of the positioning point under the action of gravity δp =( d x , d y , d z ) T After the spatial position difference calculation is completed, the attitude of the parallel attitude adjustment system is calculated considering the influence of gravity. The attitude error caused by gravity is calculated as follows: P represents the center of mass position of the parallel attitude adjustment system under the action of gravity, R represents the attitude transformation matrix of the platform relative to the global coordinate system under the action of gravity, then:

[0035] p+δp = P + Rp t

[0036] in, p Indicates the coordinates of the positioning point in the global coordinate system. δp Indicates the coordinate change of the center point of the work platform in the global coordinate system,p t Represents the coordinates of the positioning point in the work platform coordinate system. After measuring the coordinates of multiple positioning points on the platform, the particle swarm algorithm is used to fit the posture considering the influence of gravity, and the posture error caused by gravity is calculated by subtracting it from the posture without considering the influence of gravity. Y 1=( δx 1, dy 1, δz 1, yes 1, db 1, dg 1) T ,in, δx 1. dy 1. δz 1 represents the platform in the global coordinate system x 、 y 、 z Position error in direction, yes 1. db 1. dg 1 represents the platform around the global coordinate system x 、 y 、 z The attitude error of the axis.

[0037] (2) The multi-body dynamics method is used to perform dynamic modeling on the parallel attitude adjustment system and calculate the force at the spherical joint. Each POGO column is simplified into a cantilever beam. According to the calculation equation of the cantilever beam in material mechanics, the spatial deformation of the spherical joint under the force at the spherical joint is calculated. The particle swarm algorithm is used to calculate the work platform posture error caused by the deformation of the rod caused by the force at the spherical joint. Y 2=( δx 2, dy 2, δz 2, yes 2, db 2, dg 2) T ,in, δx 2. dy 2. δz 2 respectively represent the platform in the global coordinate system x 、 y 、 z Position error in direction, yes 2. db 2. dg 2 respectively represent the platform around the global coordinate system x 、 y 、 z The attitude error of the axis.

[0038] (3) Based on the dynamic model of step (2), calculate the position error of the follower moving pair, and use a method similar to the calculation of the posture error caused by the force at the ball joint to calculate the posture error of the working platform caused by the position error. Y 3=( δx 3, dy 3, δz 3, yes 3, db 3, dg 3) T ,in, δx 3. dy 3. δz 3 represent the platform in the global coordinate system x 、 y 、 z Position error in direction, yes 3. db 3. dg 3 represent the platform around the global coordinate system x 、 y 、 z The attitude error of the axis.

[0039] (4) Ignore the high-order terms in the posture error, add the posture errors caused by gravity, the force at the spherical joint, the position error, etc., and calculate the posture error caused by elastic deformation Y t .

[0040] Y t = Y 1+ Y 2+ Y 3

[0041] The corresponding position error matrix is:

[0042] Y p =( δx 1+ δx 2+ δx 3, dy 1+ dy 2+ dy 3, δz 1+ δz 2+ δz 3) T

[0043] The corresponding attitude error matrix is:

[0044]

[0045] (5) Ignoring the influence of high-order terms, the total pose error matrix is ​​subtracted from the pose error matrix caused by elastic deformation to obtain the pose error matrix caused by structural error Y s The conventional calibration method is to use a laser tracker or other measuring device to fit the pose error, without considering the influence of elastic deformation. This invention considers the influence of elastic deformation on the calibration results, and separates the pose error caused by structural error from the pose error caused by elastic deformation:

[0046] Y s = Y - Y t

[0047] in, Y s Represents the pose error caused by structural error.

[0048] The posture error caused by structural error is separated from the posture error caused by elastic deformation, and then kinematic calibration is performed. The structural error of the parallel posture adjustment system is identified. The error model of the parallel posture adjustment system is expressed as:

[0049] K 1 X = K 2 Y

[0050] in, K 1. K 2 represents the coefficient matrix, X represents the structural error data matrix, Y Represents the pose error matrix. The coefficient matrix is ​​derived through matrix operations. The coordinates of the upper positioning point of the work platform are measured using a laser tracker or other equipment. Based on the three-point positioning principle, the pose error of the work platform in different spatial poses is calculated using a pose fitting algorithm.

[0051] (6) Ideal structural parameters X ideal Subtract the identified structural error X , and obtain the modified structural parameters X ac , that is, the actual structural parameters X ac .

[0052] X ac = X ideal －X

[0053] (7) Considering the posture error caused by elastic deformation Y tWhen compensating for positioning error, the target posture T id Perform secondary positioning; the secondary positioning method is to subtract the pose error matrix caused by elastic deformation from the target pose matrix to obtain the new pose that needs to be adjusted for error compensation T ac :

[0054] T ac = T id －Y t

[0055] (8) In the modified structural parameters T ac Based on the actual structural parameters X ac Perform kinematic inverse analysis to obtain the movement distance of each moving pair, and then control the movement of each moving pair to perform error compensation.

[0056] (9) Furthermore, machine learning methods are used to establish the correlation between the target positioning posture and the motion of the moving pair, and to train the parallel attitude adjustment system's autonomous high-precision positioning capability.

[0057] The parts not involved in the present invention are the same as the existing technology or can be implemented by using the existing technology.

Claims

1. A kinematic calibration and positioning error compensation method considering mechanism deformation, characterized by: The deflection of each point on the simply supported beam is calculated using the superposition method. The calculation results of the superposition method are compared with the finite element simulation results. The deformation difference is calculated and compensated. Combined with the particle swarm algorithm, the posture error caused by the deformation of the work platform is calculated. Based on the multi-body dynamics modeling method, the force acting on the telescopic rod and the friction force at the follower moving joint are analyzed; Based on the support force acting on the telescopic rod ball joint, the deformation of the telescopic rod is calculated in a cantilever beam manner, and the posture error caused by the support force is further calculated; based on the friction force at the follower moving joint, the deformation of the telescopic rod is calculated, and then the posture error caused by the friction force is calculated; The posture errors caused by gravity, friction and support force are added together to obtain the posture error caused by elastic deformation; during the test, the posture error caused by elastic deformation is subtracted from the total posture error to obtain the posture error caused by structural error; the posture error caused by structural error is input into the error model, and kinematic calibration is performed to identify the structural error; the ideal structural parameters are subtracted from the identified structural error to obtain the corrected structural parameters of the parallel posture adjustment system; considering the influence of the posture error caused by elastic deformation, the target posture is secondary positioned, that is, the posture error caused by elastic deformation is subtracted from the ideal target posture to obtain the target posture corresponding to the error compensation; on the basis of the corrected structural parameters, combined with the target posture of the secondary positioning, kinematic inverse solution is performed to control the motion of each moving pair and perform error compensation; further, a machine learning method is used to establish a correlation between the target positioning posture and the motion of the moving pair, and the parallel posture adjustment system is trained to have autonomous high-precision positioning capabilities.

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